V X 4 X 0 Fig 1 Particle Approaching Potential Step I Phsi221 Homework 10 A Part 1 Consider Particles Of Mass M 1 (65.56 KiB) Viewed 22 times
V X 4 X 0 Fig 1 Particle Approaching Potential Step I Phsi221 Homework 10 A Part 1 Consider Particles Of Mass M 2 (87.04 KiB) Viewed 22 times
V(x) 4 + X 0 FIG. 1: Particle approaching potential step. I. PHSI221 HOMEWORK 10 A. part 1 Consider particles of mass m and kinetic energy E > 0) approaching a potential step of -V. (Vo a positive number) from the left as indicated in Figure 1. 1. show that the function A exp (ikx) + B exp(-ikx) where A and B are constants and k= V2mE, h is a solution to the time independent Schrödinger equation for r < 0 2. Give the fraction of the particles that is reflected back by the potential step.
B. part 2 Hermitian operators and hermitian conjugates 1. Show the following three identities for any two operators A and B and a complex number c: + = + (a) (AB)' = BA (b) (A+B)* – B+ À (c) (cA)* = c A + + =c* 2. Use the above to find the hermitian conjugate of the kinetic energy operator. Is it hermitian? 3. Find the hermitian conjugate of a+. Is it hermitian?
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